“In science, patterns are observations of any non-random structure. In ecology for example, a pattern has long been understood as the “structure which results from the distributions of organisms in, or from, their interactions with their environments” (Hutchinson 1953, p.3, also see Watt 1947, Greig-Smith 1979). However, when identifying patterns in nature, scientists more precisely mean the identification of patterns in data about nature. Important considerations for identifying patterns, therefore, are the means by which data were collected, and most importantly the scales of measurement used to collect data. In particular, two components of scale – grain and extent – are important in determining whether a pattern is identified. Grain is the resolution of measurement (i.e. the smallest unit of measurement at which objects or states can be distinguished), whereas extent is the full scope of observation or total range over which measurements are made. As examples, different spatial patterns will be detectable in maps of vegetation configuration in semi-arid areas depending on the grain and extent of the maps (e.g. compare Figures 3 and 6 in Barbier et al. 2006), and different temporal patterns will be detectable in storm hydrographs depending on the resolution and duration of measurement (e.g. compare drainage for 10 minute intervals with full 80 minute duration, and observed drainage with simulated drainage, in Figure 5 of Mueller et al. 2007). In other circumstances, observed structures may be described as being ‘scale-free’. These structures lack a characteristic length scale and have the same properties across any grain and extent of measurement (e.g. power-law distributions of vegetation patch sizes; Kéfi et al. 2007). These scale-free structures can also be considered to be patterns.

Because patterns are non-random, they have the potential to provide information. In natural science this information is usually understood as being about the processes that caused the pattern. Thus, identifying patterns is useful because they can be used to investigate processes (Levin 1992). Processes are typically assumed to act at a different scale from the patterns they produce, with patterns either emerging from processes at smaller scales (‘bottom-up’ processes) or imposed by constraints at larger scales (‘top-down’ processes). It is also important to consider the reciprocal effects of patterns on processes (Turner 1989). For example, the field of landscape ecology has placed an emphasis on the quantification of spatial pattern using pattern metrics (e.g. McGarigal 2006) and shown how the history of previous ecological processes can increase the strength and extent of spatial pattern (Peterson 2002). The ‘pattern-oriented modelling’ (POM) approach has been developed to use models to help decode the information present in patterns to better understand processes (Wiegand et al. 2003, Grimm et al. 2005). The POM approach iteratively compares empirical and model-output patterns at multiple scales and levels of organization and for multiple models to identify most appropriate models. Approaches like POM, which place pattern at the centre of scientific investigation, are vital for improving understanding about physical processes.”